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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::Rational;
use crate::gaussian_rational::GaussianRational;
use malachite_base::num::arithmetic::traits::{
CanonicalPrimitivePart, CanonicalizeUnit, ContentAndCanonicalPrimitivePart,
ContentAndPrimitivePart, PrimitivePart,
};
use malachite_nz::gaussian_integer::GaussianInteger;
impl CanonicalPrimitivePart for GaussianRational {
type Output = GaussianInteger;
/// Computes the canonical primitive part of a [`GaussianRational`], taking the
/// [`GaussianRational`] by value.
///
/// This is the [`primitive_part`](PrimitivePart::primitive_part), a [`GaussianInteger`] with
/// coprime parts, multiplied by the power of $i$ that brings it into canonical unit form, as
/// [`canonicalize_unit`](CanonicalizeUnit::canonicalize_unit) chooses it for a
/// [`GaussianInteger`]: the associate whose argument lies in $(-\pi/4, \pi/4]$. So the four
/// associates of a Gaussian rational all have the same canonical primitive part. Zero's is
/// zero.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("-1/2+3i/4").unwrap();
/// assert_eq!(x.canonical_primitive_part().to_string(), "3+2i");
/// ```
#[inline]
fn canonical_primitive_part(self) -> GaussianInteger {
self.primitive_part().canonicalize_unit()
}
}
impl CanonicalPrimitivePart for &GaussianRational {
type Output = GaussianInteger;
/// Computes the canonical primitive part of a [`GaussianRational`], taking the
/// [`GaussianRational`] by reference.
///
/// This is the [`primitive_part`](PrimitivePart::primitive_part), a [`GaussianInteger`] with
/// coprime parts, multiplied by the power of $i$ that brings it into canonical unit form, as
/// [`canonicalize_unit`](CanonicalizeUnit::canonicalize_unit) chooses it for a
/// [`GaussianInteger`]: the associate whose argument lies in $(-\pi/4, \pi/4]$. So the four
/// associates of a Gaussian rational all have the same canonical primitive part. Zero's is
/// zero.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalPrimitivePart;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("-1/2+3i/4").unwrap();
/// assert_eq!((&x).canonical_primitive_part().to_string(), "3+2i");
/// ```
#[inline]
fn canonical_primitive_part(self) -> GaussianInteger {
self.primitive_part().canonicalize_unit()
}
}
impl ContentAndCanonicalPrimitivePart for GaussianRational {
type Content = Rational;
type CanonicalPrimitivePart = GaussianInteger;
/// Splits a [`GaussianRational`] into its content and its canonical primitive part, taking the
/// [`GaussianRational`] by value.
///
/// See [`content_and_primitive_part`](ContentAndPrimitivePart::content_and_primitive_part) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let (content, primitive) = GaussianRational::from_str("-1/2+3i/4")
/// .unwrap()
/// .content_and_canonical_primitive_part();
/// assert_eq!(content.to_string(), "1/4");
/// assert_eq!(primitive.to_string(), "3+2i");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Rational, GaussianInteger) {
let (content, primitive) = self.content_and_primitive_part();
(content, primitive.canonicalize_unit())
}
}
impl ContentAndCanonicalPrimitivePart for &GaussianRational {
type Content = Rational;
type CanonicalPrimitivePart = GaussianInteger;
/// Splits a [`GaussianRational`] into its content and its canonical primitive part, taking the
/// [`GaussianRational`] by reference.
///
/// See [`content_and_primitive_part`](ContentAndPrimitivePart::content_and_primitive_part) and
/// [`canonical_primitive_part`](CanonicalPrimitivePart::canonical_primitive_part); the content
/// is found once rather than twice.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the numerators and denominators of the real and imaginary parts of `self`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ContentAndCanonicalPrimitivePart;
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// let x = GaussianRational::from_str("-1/2+3i/4").unwrap();
/// let (content, primitive) = (&x).content_and_canonical_primitive_part();
/// assert_eq!(content.to_string(), "1/4");
/// assert_eq!(primitive.to_string(), "3+2i");
/// ```
#[inline]
fn content_and_canonical_primitive_part(self) -> (Rational, GaussianInteger) {
let (content, primitive) = self.content_and_primitive_part();
(content, primitive.canonicalize_unit())
}
}